Local Approaches to DisorderDriven MetalInsulator Transitions

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Local Approaches to Disorder-Driven
Metal-Insulator Transitions
Vladimir Dobrosavljevic Department of Physics
and National High Magnetic Field
Laboratory Florida State University
Collaborators Darko Tanaskovic (FSU) Maria
Carolina de Oliveira Aguiar (FSU) Andrei Pastor
(FSU) Branislav Nikolic (Georgetown?
Delaware) Eduardo Miranda (Campinas, Brazil) Gabi
Kotliar (Rutgers) Elihu Abrahams (Rutgers)
Funding NHMFL/FSU Alfred P. Sloan Foundation NSF
grant DRM-9974311
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Contents

• The metal-insulator transition a bit of history
• Experiments SiP, Mooij correlation, the
  apparent ? MIT in 2D
• Order parameter description DMF theory
• Correlation-enhanced disorder screening
  (metallic phase in 2D?)
• DMFTlocalization Anderson-Mott transition
• Typical medium theory of localization
• (Can also include glassy behavior not
  presented today)

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Metal-insulator transition a quantum critical
point?

• Experiment
• Sharp transition at T0
• Continuous transition

• Theoretical problems
• No small parameter
• No symmetry breaking
• Order parameter??

• A way out controlled expansion around d2?
  (LCD)
• Scaling theory of localizationinteraction, sigma
  model,
• Limitations
• (disordered) Fermi liquid, low temperatures,
  small critical region (?)
• No strong correlation effects, NFL, metastability
  (glass)

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Experiments
A15 compounds
Doped semiconductors
?? (n-nc)1/2
nc
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The 2D Metal-Insulator Transition??
(Silicon MOSFET Kravchenko et al., 1995-2002)

• Was forbidden by the gang of 4 some 20 years
  ago ?
• But drastic change of behavior near nc!!!
• NOTE behavior seen up to T 0.25 TF broad
  density range

Mass enhanced But not the g-factor Large
resistivity drop!
TF 10K
Metal destroyed by small parallel field near
transition Low density rs 10 Close to Wigner
crystal?
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Experiments demand Need theory valid over a
broad parameter range Mean-field theory, not
long-wavelength (RG) theory (Gaussian
fixed-points have scaling too) Likely to have
strong correlation effects Temperature range
beyond Fermi liquid regime Combination of
correlation, localization and glassy physics My
claim extended DMFT meets all these conditions!
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Dynamical Mean-Field Theory -Physics Behind the
Equations-

• MIT - a dynamical phase transition (transport,
  not static order critical)

What should be the order parameter? -Go back to
basic principles-

• Order parameter escape (transition) rate from
  lattice site

• Hubbard model, random site energies (Wigner
  crystal Mott insulator correlated
  metal)

• Effective local dynamical theory

Integrate out all sites but one
self-consistency condition
Local DOS
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Disordered Metallic Phase Correlation-Induced
Screening of Randomness (work in progress)
Choose disorder W U, reduce EF (ignore
localization CPA)

• Resistivity drop at low T
• temperature-dependent screening?
• Altshuler Maslov,
• Das Sarma Hwang,
• Dolgopolov Gold,
• Herbut, Aleiner et al.

• H-F theory
• weak T-dependence, only factor 2 drop
• (solve DMFT in H-F, similar as others)

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Full DMFT theory

• Strong T-dependence,
• factor gt 10 drop!!!
• (solve full DMFT
• using IPT or slave bosons)
• Enhanced screening at low T
• due to correlations
• (approach to Mott transition)
• Strong inelastic scattering
• at higher T

Scattering rate 1/?
T/TF

• Incoherent Fermi liquid (low T TF/m
  distribution of local coherence scales TK)

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Approaching the Anderson-Mott transition
Localization Effects

• Localization effects in DMFT local DOS
  statistics.

(a) Standard DMFT (large coordination)
For U0 get CPA ( Drude) No localization!!!
(b) Extended DMFT (finite coordination, Bethe
lattice)
Order parameter
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Intermediate Disorder an Electronic Griffiths
Phase (V.D. G. Kotliar, PRL 1997 E. Miranda
V.D, PRL 2001)

• Quasiparticle
• Electron "cloud" (drags back)

• Disordered systems
• Quasiparticle weight Z 1/m
• is position dependent !!
• Localization effects
• "near" Anderson-Mott transition
• Very broad distribution P(Zi)
• Some (rare) regions ? Huge contributions to c, g
  ("Griffiths phases")
• Leads to disorder-driven non-Fermi liquid
  behavior (metals)
• ? ?(W) is a smooth function of disorder W
  changes sign at W gt WNFL
• seen in doped semiconductors, Kondo alloys, e.
  g. UCu5-xPdx c g T-a (a 0.1-0.3)

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DMFT Picture of the Anderson-Mott
Transition (doped Mott insulator disorder V.D.
G. Kotliar, PRL 1997 in progress)
Mott-like order parameter Typical quasiparticle
weight
Anderson-like order parameter Typical local DOS
conductivity

Small energy scale
T TF Ztyp ? 0
Ztyp
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Typical medium theory a local order-parameter
picture of localization (V. D. , Pastor,
Nikolic)

• So far mean-field treatment of interactions,
  numerical (Bethe lattice) of localization
• Goal mean-field (order-parameter) treatment of
  both interactions localization
• Idea local picture of localization (Anderson,
  1958 Abou-Chacra, Anderson, Thouless, 1971)
• Problem with CPA wrong order parameter (average
  DOS noncritical)
• Order parameter typical DOS, self-consistently
  calculated in DMFT-like fashion
• CLAIM reproduces most expected features of
  Anderson transition
• Can easily add interactions using DMFT

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TMT Formalism

• DMFT-like philosophy
• single site effective medium defined by
  self-energy ?(?)
• Local Greens function
• Cavity function
• Typical DOS

Results phase diagram
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Quantitative accuracy transport

• Comparison with exact numerics
• (exact diagonalization, finite size scaling, 3D
  cubic lattice)
• NOTE no adjustable parameters!

• Conductivity Mooij correlation,

?TMM
Inelastic scattering rate
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Conclusions

• Extended DMFT order-parameter theory for
  Anderson-Mott transition
• Non-perturbative approach to correlations in
  disordered systems
• Metallic phase enhanced disorder screening (low
  T) inelastic scattering (high T)
• Non-Fermi liquid behavior as precursor to MIT
  two-fluid behavior
• New physical picture of MIT in correlated
  disordered systems
• Can also incorporate glassy behaviors of
  electrons (not described today)
• Consistent with experiments in doped
  semiconductors, Kondo alloys, MOSFETs,